Quasi-normal modes in coupled systems

1993 ◽  
Vol 10 (10) ◽  
pp. 2067-2076 ◽  
Author(s):  
T W Baumgarte ◽  
B G Schmidt
Keyword(s):  
Normal Modes ◽  
Coupled Systems

Coupled Oscillators and Synchronization

2019 ◽  
pp. 177-204
Author(s):  
David D. Nolte
Keyword(s):  
Phase Locking ◽  
Beat Frequency ◽  
Normal Modes ◽  
Coupled Systems ◽  
Torus Action ◽  
Slow Phase ◽  
Nonlinear Coupling ◽  
Frequency Locking ◽  
Frequency Entrainment ◽  
Central Paradigm

Coupled linear oscillators provide a central paradigm for the combined behavior of coupled systems and the emergence of normal modes. Nonlinear coupling of two autonomous oscillators provides an equally important paradigm for the emergence of collective behavior through synchronization. Simple asymmetric coupling of integrate and fire oscillators captures the essence of frequency locking. Quasiperiodicity on the torus (action-angle oscillators) with nonlinear coupling demonstrates phase locking, while the sine-circle map is a discrete map that displays multiple Arnold tongues at frequency-locking resonances. External synchronization of a phase oscillator is analyzed in terms of the “slow” phase difference, resulting in a beat frequency and frequency entrainment that are functions of the coupling strength.

A POD-Based Identification of the Reduced Dynamics of an Exact Nonlinear Rod Loaded Transversely

2003 ◽  
Author(s):  
Ioannis T. Georgiou ◽  
Christos E. Kanavis
Keyword(s):  
Normal Modes ◽  
Coupled Systems ◽  
Critical Parameters ◽  
Reduced Model ◽  
Order System ◽  
Element Approximation ◽  
Low Frequencies ◽  
Wide Range ◽  
Proper Orthogonal ◽  
Qualitative Changes

Reduced dynamics of a nonlinear exact rod is derived by restricting the coupled nonlinear equations of motion onto Proper Orthogonal Modes (POD) identified by a Proper Orthogonal Decomposition of the finite element approximation to the dynamics. For the case of a dominant POD mode, the reduced dynamical system is a geometrically exact nonlinear oscillator. Numerical integration reveals that the phase portrait of the reduced system, for the case of zero dissipation, has Hamiltonian structure. For harmonic forcing at low frequencies, the reduced system predicts exceptionally well the dynamics of the nonlinear rod over a wide range of forcing amplitude. For forcing frequencies in the order of the fundamental frequency for linear bending motions, the reduced model predicts very well the qualitative changes of the dynamics but it underestimates the critical parameters at which the qualitative changes occur at high levels of forcing amplitudes. It is conjectured that the reduced model stemming from the restriction of the full order system onto a single dominant POD describes the dynamics of a nonlinear normal mode of vibration. The POD method can be used to identify the normal modes of vibration of coupled systems with complicated nonlinearities.

Terrorist teams as loosely coupled systems.

2018 ◽  
Vol 73 (4) ◽  
pp. 491-503 ◽  
Author(s):  
Matthias Spitzmuller ◽  
Guihyun Park
Keyword(s):  
Coupled Systems ◽  
Loosely Coupled Systems ◽  
Loosely Coupled

Filtering methods for finite-time normal modes and atmospheric error growth

2000 ◽  
Vol 42 ◽  
pp. 1482
Author(s):  
Mozheng Wei ◽  
Jorgen S. Frederiksen ◽  
Steve Kepert
Keyword(s):  
Finite Time ◽  
Normal Modes ◽  
Error Growth

Gravitational Waves

2018 ◽  
Author(s):  
Michele Maggiore
Keyword(s):  
Black Hole ◽  
Perturbation Theory ◽  
Gravitational Waves ◽  
Transfer Functions ◽  
Normal Modes ◽  
Cosmological Perturbation ◽  
Tests Of General Relativity ◽  
Pulsar Timing ◽  
Tensor Perturbations ◽  
Stochastic Backgrounds

A comprehensive and detailed account of the physics of gravitational waves and their role in astrophysics and cosmology. The part on astrophysical sources of gravitational waves includes chapters on GWs from supernovae, neutron stars (neutron star normal modes, CFS instability, r-modes), black-hole perturbation theory (Regge-Wheeler and Zerilli equations, Teukoslky equation for rotating BHs, quasi-normal modes) coalescing compact binaries (effective one-body formalism, numerical relativity), discovery of gravitational waves at the advanced LIGO interferometers (discoveries of GW150914, GW151226, tests of general relativity, astrophysical implications), supermassive black holes (supermassive black-hole binaries, EMRI, relevance for LISA and pulsar timing arrays). The part on gravitational waves and cosmology include discussions of FRW cosmology, cosmological perturbation theory (helicity decomposition, scalar and tensor perturbations, Bardeen variables, power spectra, transfer functions for scalar and tensor modes), the effects of GWs on the Cosmic Microwave Background (ISW effect, CMB polarization, E and B modes), inflation (amplification of vacuum fluctuations, quantum fields in curved space, generation of scalar and tensor perturbations, Mukhanov-Sasaki equation,reheating, preheating), stochastic backgrounds of cosmological origin (phase transitions, cosmic strings, alternatives to inflation, bounds on primordial GWs) and search of stochastic backgrounds with Pulsar Timing Arrays (PTA).

Triatomic molecules

2018 ◽  
Author(s):  
John H. D. Eland ◽  
Raimund Feifel
Keyword(s):  
Degrees Of Freedom ◽  
Normal Modes ◽  
Electronic States ◽  
Triatomic Molecules ◽  
Doubly Charged Ions ◽  
Spectral Bands ◽  
Valence Electrons ◽  
Doubly Charged ◽  
Charged Ions ◽  
Double Ionisation

Double ionisation of the triatomic molecules presented in this chapter shows an added degree of complexity. Besides potentially having many more electrons, they have three vibrational degrees of freedom (three normal modes) instead of the single one in a diatomic molecule. For asymmetric and bent triatomic molecules multiple modes can be excited, so the spectral bands may be congested in all forms of electronic spectra, including double ionisation. Double photoionisation spectra of H2O, H2S, HCN, CO2, N2O, OCS, CS2, BrCN, ICN, HgCl2, NO2, and SO2 are presented with analysis to identify the electronic states of the doubly charged ions. The order of the molecules in this chapter is set first by the number of valence electrons, then by the molecular weight.

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

scholarly journals Revealing the Challenges of Smart Rainwater Harvesting for Integrated and Digital Resilience of Urban Water Infrastructure

Water ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 1902
Author(s):  
Martin Oberascher ◽  
Aun Dastgir ◽  
Jiada Li ◽  
Sina Hesarkazzazi ◽  
Mohsen Hajibabaei ◽  
...  
Keyword(s):  
Large Scale ◽  
Rainwater Harvesting ◽  
Data Communication ◽  
Integrated System ◽  
Coupled Systems ◽  
Urban Resilience ◽  
System Failures ◽  
Household Level ◽  
Performance Improvements ◽  
Smart Water

Smart rainwater harvesting (RWH) systems can automatically release stormwater prior to rainfall events to increase detention capacity on a household level. However, impacts and benefits of a widespread implementation of these systems are often unknown. This works aims to investigate the effect of a large-scale implementation of smart RWH systems on urban resilience by hypothetically retrofitting an Alpine municipality with smart rain barrels. Smart RWH systems represent dynamic systems, and therefore, the interaction between the coupled systems RWH units, an urban drainage network (UDN) and digital infrastructure is critical for evaluating resilience against system failures. In particular, digital parameters (e.g., accuracy of weather forecasts, or reliability of data communication) can differ from an ideal performance. Therefore, different digital parameters are varied to determine the range of uncertainties associated with smart RWH systems. As the results demonstrate, smart RWH systems can further increase integrated system resilience but require a coordinated integration into the overall system. Additionally, sufficient consideration of digital uncertainties is of great importance for smart water systems, as uncertainties can reduce/eliminate gained performance improvements. Moreover, a long-term simulation should be applied to investigate resilience with digital applications to reduce dependence on boundary conditions and rainfall patterns.

Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness

2021 ◽  
pp. 014233122110009
Author(s):  
Xin Meng ◽  
Baoping Jiang ◽  
Cunchen Gao
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Coupled Systems ◽  
Projective Synchronization ◽  
Slave System ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Strong Connectedness ◽  
Master System ◽  
Error System

This paper considers the Mittag-Leffler projective synchronization problem of fractional-order coupled systems (FOCS) on the complex networks without strong connectedness by fractional sliding mode control (SMC). Combining the hierarchical algorithm with the graph theory, a new SMC strategy is designed to realize the projective synchronization between the master system and the slave system, which covers the globally complete synchronization and the globally anti-synchronization. In addition, some novel criteria are derived to guarantee the Mittag-Leffler stability of the projective synchronization error system. Finally, a numerical example is given to illustrate the validity of the proposed method.

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